Alzheimer’s disease (AD) presents a perplexing question: why does its development span decades, even though individual amyloid beta (Aβ) deposits (senile plaques) can form rapidly in as little as 24 hours, as recent publications suggest? This study investigates whether the formation of senile plaques can be limited by factors other than polymerization kinetics alone. Instead, their formation may be limited by the diffusion-driven supply of Aβ monomers, along with the rate at which the monomers are produced from amyloid precursor protein (APP), and the rate at which Aβ monomers undergo degradation. A mathematical model incorporating the nucleation and autocatalytic process (via the Finke-Watzky model), as well as Aβ monomer diffusion, was proposed. The obtained system of partial differential equations was solved numerically, and a simplified version was investigated analytically. The computational results predicted that it takes approximately 7 years for Aβ aggregates to reach a neurotoxic concentration of 50 μM. Additionally, a sensitivity analysis was performed to examine how the diffusivity of Aβ monomers and their production rate impact the concentration of Aβ aggregates.

中文翻译：

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β淀粉样蛋白单体扩散性对老年斑形成的影响

阿尔茨海默病 (AD) 提出了一个令人困惑的问题：尽管正如最近的出版物所表明的那样，单个淀粉样蛋白 (Aβ) 沉积物（老年斑）可以在短短 24 小时内迅速形成，但为什么它的发展要跨越数十年？这项研究调查了老年斑的形成是否可以受到聚合动力学以外的因素的限制。相反，它们的形成可能受到 Aβ 单体的扩散驱动供应、淀粉样前体蛋白 (APP) 产生单体的速率以及 Aβ 单体降解的速率的限制。提出了一个结合成核和自催化过程（通过 Finke-Watzky 模型）以及 Aβ 单体扩散的数学模型。对所获得的偏微分方程组进行了数值求解，并对简化版本进行了分析研究。计算结果预测，Aβ 聚集体达到 50 μM 的神经毒性浓度大约需要 7 年时间。此外，还进行了敏感性分析，以检查 Aβ 单体的扩散性及其生产率如何影响 Aβ 聚集体的浓度。